What are hydronium and hydroxide ions?

Hydroxide $=$ $O {H}^{-}$; hydronium ion is represented as ${H}^{+}$ or ${H}_{3} {O}^{+}$.
The hydronium ion and the hydroxide are respectively the characteristic cation, and anion of water. The constitution of the hydronium ion is debatable. As far as anyone knows, it is 3 or 4 water molecules with an extra proton tacked on, say ${\left({O}_{3} {H}_{7}\right)}^{+}$. It is simpler to represent the hydronium ion as ${H}_{3} {O}^{+}$ or even as ${H}^{+}$. Can you quote the equilibrium reaction that governs formation of these ions in water?